Question

Human measurements provide a rich area of application for statistical methods. In a longitudinal study the development of elementary school children explored the relationship between IQ and private speech. Private speech is considered to be when children talk to themselves. It was thought that private speech would be related to IQ, because IQ is supposed to measure mental maturity, and it was known that private speech decreases as students progress through the primary grades. The study included 34 students whose first-grade IQ scores are given below.

######################################################################
# Use the R code to calculate the sample summary statistics, histogram and boxplot.
# Can copy and paste directly to R script.

IQ.data = c(77,	90,	99,	102,	103,	103,	105,	106,	106,	106,	107,	107,
109,	109,	112,	112,	114,	114,	114,	115,	116,	116,	118,	118,
124,	124,	125,	126,	127,	132,	136,	140,	140,	150)

summary(IQ.data)
sd(IQ.data)
hist(IQ.data)
boxplot(IQ.data, horizontal = TRUE)
######################################################################
Enter the values for the mean, standard deviation and five number summary. Round your answers to 1 decimal place.

Mean	s

Minimum	Q1	Median	Q3	Maximum

Based on the histogram and boxplot from R, choose the following statements that correctly describe the IQ scores. Hint: Five are correct statements. (Select all that apply.)

The distribution of IQ scores has an interquartile range from 106 to 124 .

The typical IQ score is around 114.

The distribution of IQ scores is nearly symmetric.

The lowest IQ, 77, stands out as a low outlier.

The distribution of IQ scores is very negatively skewed.

The second lowest IQ, 90, is the smallest value that isn't an outlier.

The boxplot indicates no outliers.

The distribution of IQ scores has an interquartile range from 77 to 150 .

The boxplot indicates 4 outliers.

The second lowest IQ, 90, stands out as an outlier.

The typical IQ score is around 118.

The distribution of IQ scores is very positively skewed.

Answer 1

R-code:

Mean = 114.7647

Five Number Summary:

Min. 1st Qu. Median Mean 3rd Qu. Max.
  77.0 106.0 114.0 114.8 124.0 150.0

Histogram:

Boxplot:

Correct answers:

The distribution of IQ scores has an inter-quartile range from 106 to 124 .

The typical IQ score is around 114.

The distribution of IQ scores is nearly symmetric.

The lowest IQ, 77, stands out as a low outlier.

The second lowest IQ, 90, is the smallest value that isn't an outlier.