Question

66 randomly selected students were asked the number of pairs of shoes they have. Let X representthe number of pairs of shoes. The results are as follows:# of Pairs of Shoes 4Frequency 75 68 9 10 114 11 11 11 2 12 8Round all your answers to 4 decimal places where possible.The mean is:The median is:The sample standard deviation is:The first quartile is:The third quartile is:What percent of the respondents have at least 10 pairs of shoes?9617% of all respondents have fewer than how many pairs of shoes?

Answer 1

Given data

1. The mean

`(\sum fx)/(\sum f)=(505)/(66)=7.6515`

2. The median

`\begin{gathered} \text{ Median = (}\frac{\text{N+1}}{2})th \\ =((66+1)/(2))th=((67)/(2))th=33.5th \\ \text{The median is the 33.5th }term\text{ which is between 7 and 8} \\ \text{The median is }\frac{\text{7+8}}{2}=(15)/(2)=7.5 \end{gathered}`

3. The sample standard deviation

`\begin{gathered} SD\text{ =}\sqrt[]{\frac{\sum f|x-\bar{x}|}{\sum f}} \\ \bar{x}=7.6515 \\ SD=\sqrt[]{4.8028} \\ SD=2.1915 \end{gathered}`