Question

What is the median, mode, mean and range of 17, 19, 22, 22, 27, 31, 35, 37, 45, 98?

Answer 1

Hint: To obtain the median, mode and range of the given data set. Firstly assign the given data in ascending order then firstly we will find the median which is equal to the middle value. Then we will find the mode which is the value repeated most. For mean we will add all the values and divide it by the number of values. Finally for range we will subtract the lowest value from the highest value and get the desired answer.

Complete step by step solution:
The data is given as:
$17,19,22,22,27,31,35,37,45,98$
Now as we can see they are already in ascending order.
So firstly we will find the median.
As the data set has an even number we will find the mean of the middle term for our median.
$17,19,22,22,\underline{27,31},35,37,45,98$
Median $=\dfrac{27+31}{2}$
Median $=29$
Next, we will find the mode.
As we can 22 is repeated twice which is the most time a term is repeated
$17,19,\underline{22,22},27,31,35,37,45,98$
Mode $=22$
Next, we will find the mean as follows:
Mean $=\dfrac{17+19+22+22+27+31+35+37+45+98}{10}$
Mean $=$$\dfrac{353}{10}$
Mean $=35.3$
Lastly we will find the range as follows:
Range = Highest value – Lowest value
Range $=98-17$
Range $=81$

Hence the median, mode, mean and range of 17, 19, 22, 22, 27, 31, 35, 37, 45 and 98 is $29,22,35.3,81$ respectively.

Note: Mean of a data set is none other than the average where we add all the terms and divide it by the number of terms. Median is the middle value if the number of terms is odd and if the number of terms is even it is equal to the mean of two middle values. Mode is the value which is repeated most in the data set. Range is the spread of the data from the lowest to highest value.