Question

65 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 4 5 6 7 8 9 10 11 12Frequency 5 6 12 7 9 7 7 7 5Round 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 12 pairs of shoes?%0% of all respondents have fewer than how many pairs of shoes?

Answer 1

Step 1: Write out the formula for computing mean

`\bar{x}=(\sum fx)/(\sum f)`

Where x is the variable that represent values and f is the variable that represents frequencies.

Using this formula, we can compute the mean to be 7.8923

Step 2: Compute the median using the given frequency table

The median of a distribution is the middle number of the sorted list of data

In this case the median is 8

Step 3: Compute the standard deviation using the given frequency table

The standard deviation of a data is a measure of how much the numbers in a dataset differs from their mean.

And in this case, the standard deviation is Standard deviation σ = 2.3922

Step 3: Compute the first quartile using the given frequency table

`\sum f=65`

65 ÷ 4 =16.25

So the first quartile Q₁ is between the 16th and 17th number.

The 16th number is 6 and the 17th number is also 6

Therefore,

`Q_1=(6+6)/(2)=6`

The first quartile is 6

Step 4: Compute the third quartile using the given frequency table

`\sum f=65`

3(65 ÷ 4) = 48.75

So the first quartile Q₁ is between the 48th and 49th number.

The 48th number is 10 and the 49th number is also 10

Therefore,

`Q_3=(10+10)/(2)=10`

The third quartile is 10

Step 4: Compute the percentage of students with at least 12 pairs of shoes

The phrase "at least 12 pairs of shoes" means "12 pairs of shoes or more".

Therefore, the number of students with "at least 12 pairs of shoes" is 5.

The total number of students is 65.

Hence, the frequency is given as

`(5)/(65)*100\text{ \% }\approx7.6923\text{ \%}`

The percentage of students with at least 12 pairs of shoes is 7.6923%

Also,

None of the students has fewer than 4 pairs of shoes.

Therefore, 0% of all respondents has fewer than 4 pairs of shoes

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