Human measurements provide a rich area of application for statistical methods. T

Question

Human measurements provide a rich area of application for statistical methods. The article "A" Longitudinal Study of the Development of Elementary School Children's Private Speech "T" reported on a study of children talking to themselves (private speech). 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 33 students whose first grade IQ scores are given here. Use the R code to calculate the sample summary statistics, histogram and boxplot. (Can copy and paste directly to R script.) Enter the values for the mean, standard deviation and five number summary. Describe the data and comment on any Interesting features. The lowest IQ, 82, stands out as a low outlier. The distribution of IQ scores has an interquartile range from 108 to 119. The distribution of IQ scores is slightly positively skewed. The distribution of IQ scores is very negatively skewed. The typical IQ score is around 113. The distribution of IQ scores is symmetric. The typical IQ score is around 115. The distribution of IQ scores has an interquartile range from B2 to 146. The second lowest IQ, 96, stands out as an outlier. The boxplot indicates no outliers. The boxplot indicates 4 outliers.

Explanation / Answer

From Excel,

Mean = 113.7273, std dev = 12.74331, min= 82, Q1=108, Median = 113, Q3=119, Max=146

The following statements are true:

The lowest IQ, 82, stands out as a low outlier(min is 82)

The distribution of IQ scores has an interquartile range from 108 to 119(Q1=108 and Q3=119)

The distribution of IQ scores is very negatively skewed (mode > median and mean)

The typical IQ score is around 113. (median=113)

The second lowest IQ, 96, stands out as an outlier.

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