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 Shoes475 6 74 11 118 9 10 1111 2 12 8FrequencyRound all your answers to 4 decimal places where possible,The mean is:7.6515The median is:7.5The sample standard deviation is:2.1915The first quartile is:The third quartile is:What percent of the respondents have at least 10 pairs of shoes?%17% of all respondents have fewer than how many pairs of shoes?Hint: Using a Frequency TableVideo on Using the T184 for Statistics Given a Frequency Table [+]

Answer 1

The first quartile

`\begin{gathered} Q_1=((N+1)/(4))th=((66+1)/(4))th=((67)/(4))th=16.75th \\ \text{The first quartile is the 16.75th term which is }6 \end{gathered}`

The third quartile

`\begin{gathered} Q_3=(3)/(4)(N+1)th=(3)/(4)*67th=50.25th\text{ term} \\ \text{The third quartile is the 50.25th term which is }10 \end{gathered}`

Percentage of the respondents with at least 10 pairs of shoes

`\begin{gathered} P(x\ge10)=(12+8)/(66)=(20)/(66)=(10)/(33) \\ (10)/(33)*100\text{ \%}=30.3030\text{\%} \end{gathered}`

17% of all respondents have fewer than how many pairs of shoes

`\begin{gathered} 17\text{\%}*66=11.22\text{ }\approx11 \\ \therefore11\text{ respondents have fewer than }6\text{ pairs of shoes} \end{gathered}`