Question

7. The table shows the time spent surfing the internet in one week for several students. Organize the data
and find the mean, median, and mode. 1/28, 3/20, 5/17, 7/13, 11/10, 13/7​

Answer 1

Answer: Mean of the given data is 11.625, mode is 7 and median is 10.

Given: number of student/time spent = 1/28, 3/20, 5/17, 7/13, 11/10, 13/7​

To find: Mean, median and mode of given data.

Step-by-step explanation:

Step 1: The arithmetic mean is equal to the ratio of sum of all of the given data to the number of data.

f = frequency

x = time spent

$f\ =1\ \ \ \ 3 \ \ \ 5 \ \ \ 7 \ \ \ 11 \ \ \ 13\\x\ =28 \ \ 20 \ \ 17 \ \ 13 \ \ 10 \ \ \ 7\\fx=28 \ \ 60 \ \ 85 \ \ 91 \ \ 110 \ \ 91$

mean = $Mean = \frac{\sum fx }{\sum f}=\frac{465}{40} =11.625$

Step 2: The mode is the value that appears most often in a given data set and we can use it as a measure of central tendency, just like the median and mean. Here frequency of 7 is 13, so we can say that mode = 7.

Step 3: A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it. We can calculate the median of a given data set as given below.

f = frequency

x = time spent

cf = cumulative frequency

$f\ \ \ x\ \ \ cf\\13 \ \ 7 \ \ 13\\11\ 10\ 24\\7 \ \ 13\ \ 31\\5\ \ 17 \ \ 36\\3\ \ 20 \ \ 39\\1\ \ 28 \ \ 40\\-----\\40$

median = average of  $\frac{40}{2} th$ term and $(\frac{40}{2} +1)th$ term.

median =$\frac{ (20th \ term +21th \ term)}{2}=\frac{10+10}{2} =10$

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