Question

Fourteen seniors were asked how many minutes they spent on doing their homework the previous night. The data is displayed below. Find the median and interpret the value in context. 73 75 87 65 69 62 81 64 68 101 74 71 89 87 a 74 minutes; About half of the students spent less than 74 minutes doing homework and about half spent more than 74 minutes on homework. b 73.5 minutes; About half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework. c 73 minutes; About half of the students spent less than 73 minutes doing homework and about half spent more than 73 minutes on homework. d 73.5 minutes; Most of the students spent 73.5 minutes on homework.

Answer 1

Option b is the correct choice.

Explanation:

We have been given a data set about minutes spent on doing homework the previous night by 14 seniors.

To find the median of data set, first of all we will arrange our data values from least to greatest order.

62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101.

Since our data set has an even number (14) of data points, therefore, median will be the average of middle two points, that is 7th and 8th term.

`\text{Median}=\frac{\text{7th term + 8th term}}{2}`

`\text{Median}=(73+74)/(2)`

`\text{Median}=(147)/(2)`

`\text{Median}=73.5`

Therefore, median of our given data set is 73.5.

Since median of a data set separates the higher half from the lower half of a data sample. So about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework.

Therefore, option b is the correct choice.

Answer 2

b

Explanation:

We need to find the median of:-

73 75 87 65 69 62 81 64 68 101 74 71 89 87

First, we need to arrange the numbers in ascending order as below:-

62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101

Since there are a total of 14 numbers, let's split it up into two halves (each of seven numbers)

62, 64, 65, 68, 69, 71, 73 ||| 74, 75, 81, 87, 87, 89, 101

The median would be the mean of the two middle numbers i.e. the mean of 73 and 74

Median =
`(73+74)/(2)`

=
`(147)/(2)`

= 73.5

So, about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework