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My Arabian friend showed me this (NSFW) video of a child getting shot. He also gave me some links after a quick search:

I found it rather disturbing.

He told me that this is rather common and wasn't accidental (i.e. more common than typical civilian casualties in any war).

I know its very hard to find any unbiased sources in this controversial conflict, but does anyone have any statistics on the rate of civilian deaths?

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Please remember, comments are not meant for extended discussion. Take it to chat if you have to. –  Fabian Nov 5 '12 at 7:11
    
Thanks for the editing! My English is so crappy :( –  Sebastian Godelet Nov 6 '12 at 16:01
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Why the downvote without a comment. I thought these things don't happen that much on skeptics.so ... –  Sebastian Godelet Jan 17 '13 at 8:31
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The particular incident depicted was probably not a result of IDF fire - en.wikipedia.org/wiki/Muhammad_al-Durrah_incident –  Ofir May 30 '13 at 7:10
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up vote 31 down vote accepted

Well, since no-one provided a complete answer so far I'll try to do it (though I am an Israeli, so I'm biased).

The answer to the question in the title is yes. The data I'm about to bring is taken from B'Tselem which is the "Israeli Information Center for Human Rights in the Occupied Territories".

According to the B'Tselem report, between Jan 19, 2009 (the end of "Cast Lead" operation) and Feb 28, 2011 (that is, a little over two years), 19 Palestinian minors were killed as a direct result of the armed conflict. Some of them clearly were participating in the hostilities. B'Tselem does not (so far as I could see) ask/determine whether or not the killing was accidental, but from the description it can be understood that at least some of the deaths were accidental (specifically: mortar fire isn't overly accurate.)

I should say that there isn't a statistic that is acceptable to all and even B'Tselem has come under criticism. This is unavoidable due to "fog of war" and the fact that there are (usually) several conflicting descriptions of the same event. Still I believe (and it is quite generally accepted) that B'Tselem is a reliable source of information.

The military police policy for investigating incidents involving the death and/or injury of Palestinians has been criticized by B'Tselem and led to the following IDF statement. B'Tselem also criticized the IDF open fire policy in 2002, but at no time was it suggested that the killing of children is an encouraged policy. I hope these two examples will be enough that this isn't the case. The Hebrew Wikipedia has partial information regarding the IDF open fire protocol if anyone cares to read it.

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I’ve converted my upvote into a downvote; here’s why: although the sources and numbers shown here are solid, they are not representative and misleading. 2010 and 2011 (and now 2012) were extraordinarily peaceful; previous years saw many (!) more victims. The violence seems to abate (which would be good) but this trend isn’t yet statistically significant. –  Konrad Rudolph Nov 5 '12 at 8:02
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I would add that though 'minors' and 'kids' may be considered to be technically equivalent, they have different connotations and associated emotional baggage attached. (This is an observation about reporting of these events, not a criticism of your answer) –  Benjol Nov 6 '12 at 14:05
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The body of the question has this clarification (screenshot if you can't find it for some reason http://imgur.com/b4YZ5 or if it's edited):

Does anyone have any statistics on that...

So let me try and answer that part:

Any civilian killed, especially children is tragic and it's hard to speak of it as cold statistics, but since it was requested, here is what I've gathered so far:

The statistics are debated, each side is blaming the other for bloating numbers, so it's hard to tell.

On one hand, the general evidence I've found is that the Civilian casualty ratio for the Israeli Army is not higher (and some say even lower) than other armies in recent history.

Supporting evidence:

A testimony of a British Colonel to the UN (from http://www.unwatch.org/site/apps/nlnet/content2.aspx?c=bdKKISNqEmG&b=1313923&ct=7536409):

Testifying before the United Nations, Col. Richard Kemp, a British commander, stated that: Mr. President, based on my knowledge and experience, I can say this: During Operation Cast Lead, the Israeli Defence Forces did more to safeguard the rights of civilians in a combat zone than any other army in the history of warfare. Israel did so while facing an enemy that deliberately positioned its military capability behind the human shield of the civilian population... The truth is that the IDF took extraordinary measures to give Gaza civilians notice of targeted areas, dropping over 2 million leaflets, and making over 100,000 phone calls. Many missions that could have taken out Hamas military capability were aborted to prevent civilian casualties. During the conflict, the IDF allowed huge amounts of humanitarian aid into Gaza. To deliver aid virtually into your enemy's hands** is, to the military tactician, normally quite unthinkable. **But the IDF took on those risks.

More about this:

[Colonel Richard Kemp] spoke in 2011 about Israeli operations in the Gaza War. He said that a study published by the United Nations showed "that the ratio of civilian to combatant deaths in Gaza was by far the lowest in any asymmetric conflict in the history of warfare." He stated that this ratio was less than 1:1, and compared it favorably to the estimated ratios in NATO operations in Afghanistan (3:1), western campaigns in Iraq and Kosovo (believed to be 4:1), and the conflicts in Chechnya and Serbia (much higher than 4:1, according to anecdotal evidence). Kemp argued that the low ratio was achieved through unprecedented measures by the IDF to minimize civilian casualties, which included providing warnings to the population via telephone calls, radio broadcasts and leaflets, as well as granting pilots the discretion to abort a strike if they perceived too great a risk of civilian casualties. He also stated that the civilian casualties that did occur could be seen in light of Hamas' tactical use of Gazan civilians "as human shields, to hide behind, to stand between Israeli forces and their own fighters" and strategic use of them for exploitation of their deaths in the media

And more from the same source:

The UN estimate that there has been an average three-to-one ratio of civilian to combatant deaths in such conflicts worldwide. Three civilians for every combatant killed. That is the estimated ratio in Afghanistan: three to one. In Iraq, and in Kosovo, it was worse: the ratio is believed to be four-to-one. Anecdotal evidence suggests the ratios were very much higher in Chechnya and Serbia. In Gaza, it was less than one-to-one.

Even using B'Tselem's statistics which are not the official IDF statistics, the Civilian casualty ratio for Israel is still the same or better than other armed conflicts in recent history (e.g. the Israeli army is statistically not killing more civilians than the US army, Russian army, UK army etc, and some say even less)

On the other hand there are claims that the numbers are different, such as Wikipedia.

However, the above article includes some criticism that the numbers reported by Hamas are inaccurate:

Difficulties in ascertaining an accurate Palestinian casualty count have been attributed to a number of factors. It was reported that Hamas fighters had been ordered not to wear military uniforms during the fighting.[15][16] Israeli-Arab journalist Khaled Abu Toameh wrote in The Jerusalem Post that this practice led to the over-counting of civilian casualties and under-counting Hamas military casualties, as Palestinian casualties arrived at hospitals without weapons or any other signs revealing they were actually fighters

And claims that even Hamas themselves have conflicting reports (from the same article)

In an interview published in the London-based Arabic newspaper Al Hayat (November 1, 2010), Hamas interior minister Fathi Hammad stated that around 700 of the Gaza fatalities were Hamas fighters or militants from allied groups such as Islamic Jihad. Between 200 to 300 of these were from Hamas, and a similar number were from other militant groups, along with about 150 security forces. These figures differ dramatically from those given at the time of the conflict by Hamas. As the Agence France Presse correspondent commented, "His numbers roughly match the 709 "terror operatives" the Israeli military said it had killed during the fighting, which included members of the Hamas-run police force that has patrolled Gaza since the group seized power in 2007."[23]

Having a better Combatant to Civilian ratio than US, Russia, UK does not mean that any child being killed from either side is not a tragedy, but since the OP did request for some statistics, it seems that even with the extreme numbers, the civilian casualties ratio is not higher (or even lower) than average in conflicts of similar settings.

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Depends on how much you trust media, but here is excerpt from Guardian:

The Israeli military commander in southern Gaza at the time was Colonel Pinhas "Pinky" Zuaretz. A few weeks after Corrie's death, I (as the Guardian's correspondent in Israel) spoke to him about how it was that so many children were shot by Israeli soldiers at times when there was no combat. His explanation was chilling.

At that point, three years into the second intifada, more than 400 children had been killed by the Israeli army. Nearly half were in Rafah and neighbouring Khan Yunis. One in four were under the age of 12.

I focussed on the deaths of six children in a 10-week period, all in circumstances far from combat. The dead included a 12-year-old girl, Haneen Abu Sitta, killed in Rafah as she walked home from school near a security fence around one of the fortified Jewish settlements in Gaza at the time. The army made up an explanation by falsely claiming Haneen was killed during a gun battle between Israeli forces and Palestinians.

Zuaretz conceded to me that there was no battle and that the girl was shot by a soldier who had no business opening fire. It was the same with the killings of some of the other children. The colonel was fleetingly remorseful.

Similar story from Associated Press:

Are Israelis off hook in slaying?

[...] on July 7 in the Rafah refugee camp in the Gaza Strip. Khalil Mughrabi, 11, was playing soccer with friends, and around 7 p.m. rested on mounds of sand near the nearby Israeli-Egyptian border fence. Without warning, Mughrabi was shot in the head, with none of his friends hearing the sound of shooting, one of the soccer players, Osama al-Ahras, 13, told The Associated Press. Palestinian doctors said Tuesday that Khalil was struck by a large-caliber bullet. Two more boys, ages 10 and 13, were seriously wounded in the abdomen and testicles, respectively, doctors said. [...]

And Washington Post:

"It's a little girl," a soldier watching from a nearby Israeli observation post cautioned over the military radio. "She's running defensively eastward. . . . A girl of about 10, she's behind the embankment, scared to death."

Four minutes later, Israeli troops opened fire on the girl with machine guns and rifles, the radio transmissions indicated. The captain walked to the spot where the girl "was lying down" and fired two bullets from his M-16 assault rifle into her head, according to an indictment against the officer. He started to walk away, but pivoted, set his rifle on automatic and emptied his magazine into the girl's prone body, the indictment alleged.

"This is Commander," the captain said into the radio when he was finished. "Whoever dares to move in the area, even if it's a 3-year-old -- you have to kill him. Over."

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Do Israeli soldiers kill Palestinian kids?

Yes. And, there is all kinds of evidence for this...

The Numbers

Most amazing is this site which remembers the Palestinian children killed by the IDF. Here is the lastest that was killed in May 2013.

  • Amer Nassar, 17,of Anabta, West Bank, shot and killed by IDF soldiers while protesting the death of Palestinian prisoner Maysara Abu Hamdeya in an Israeli prison

I found the link to Amer Nassar's story using Google.

Here is another great site that documents and cites its findings: If Americans Knew. It claims "1,477 Palestinian children have been killed by Israelis and 129 Israeli children have been killed by Palestinians since September 29, 2000." And, as it points out Isreael has been the target of 65 UN Resolutions.

Another source for child fatalities is the Defense for Children International (DCI). They define their number as representing children killed as a result of Israeli military and settler presence in the Occupied Palestinian Territory since the beginning of the second Palestinian uprising against occupation, or Intifada, according to DCI-Palestine's documentation. These tables do not include children killed while involved in hostilities. DCI also tracks Palestinian Children held without bail, and the Palestinian Children currently being detained. Lastly, DCI-Palestine does a great job talking about other areas of institutional racism and discrimination towards Palestinian children.

As for this infographic (maybe NSFW), it's produced with DCI-Palestine data. They find 1,397 children to have killed:

262 aged 0-8, 231 aged 9-12, 447 aged 13-15 and 457 aged 16-17.

The total number is corroborated largely by B'Selem which finds the number at 1,376 to be the amount of Palestinian children killed by Israelis.

You can also watch plenty of anecdotal cases that you'd expect with this kind of data. * YouTube video: Israeli TV airs Gaza doctor's pleas after children killed

And the incident was covered by Reuters.

"My girls were sitting at home planning their futures, talking, then suddenly they are being shelled," he said in a voice shaking with emotion.

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