(3.46) Here are the IQ test scores of 31 seventh-grade girls in a Midwest school

Question

(3.46) Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:

Data Set

Step 1:
We expect IQ scores to be approximately Normal.
Make a stemplot to check that there are no major departures from Normality.
Use stems with units of tenths.
Match your results:

Does your stemplot show departures from Normality?

Nonetheless, proportions calculated from a Normal distribution are not always very accurate for small numbers of observations.
Find the mean for these IQ scores.
Give your answer to 2 decimal places.
Fill in the blank:

Find the standard deviation for these IQ scores.
Give your answer to 2 decimal places.
Fill in the blank:

What proportions of the scores are within one standard deviation of the mean?
Give your answer to 2 decimal places.
Fill in the blank:

What proportions of the scores are within two standard deviations of the mean?
Give your answer to 2 decimal places.
Fill in the blank:

What would these proportions be in an exactly Normal distribution?

Stemplot III 7 240 8 069 9 1368 10 023334578 11 1122244489 12 08 13 02 Stemplot IV 7 24 7 8 8 69 9 13 9 68 10 023334 10 578 11 11222444 11 89 12 0 12 8 13 02 Stemplot II 7 24 7 0 8 0 8 69 9 13 9 68 10 23334 10 578 11 11222444 11 89 12 12 8 13 2 Stemplot I 7 24 8 69 9 13 9 68 10 023334 10 578 11 1122244489 12 08 13 02

Explanation / Answer

Solution

(a) The required stemplot is option last i.e.

(b) The stemplot is symmetric with two peaks

(C) Mean = 3281/31 = 105.84

Stemplot I

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