Question

Seema obtained the following scores (out of $100$) on a set of spelling tests:
$80,85,90,71,60,100$. What is her mean score?

Answer 1

From the question, we have to find the mean score of the given data. First, we have to frame a mathematical expression for the given data. Then, we have to use the formula to find the mean. Finally we get the required answer.

Formula used: The mean stands as an average. Mean is simply the average of the numbers provided.
The process of sharing out equally is the basis of average. Mean is also known as Arithmetic mean. The mean of several items is the value equally shared out among the items.
${\text{Mean = }}\dfrac{{{\text{Total of all items}}}}{{{\text{Number of items}}}}$

Complete step-by-step solution:
According to the question, we have to find the mean of the observations. Now, we are going to write in the mathematical expression.
${\text{Mean = }}\dfrac{{{\text{Total of observations}}}}{{{\text{Number of observations}}}}$
Mean is the average value for a given dataset. It is based on all the observations. It is affected by the extreme values.
Here, the data set is $80,85,90,71,60,100$
Number of observation is $6$
The total of the observation is $80 + 85 + 90 + 71 + 60 + 100 = 486$
Thus we will get the mean score if we divide the sum of the number with the total number of observations.
So, ${\text{Mean = }}\dfrac{{{\text{Total of all items}}}}{{{\text{Number of items}}}}$
Mean $= \dfrac{{486}}{6}$
On dividing we get $81$,
Hence the mean of seema’s score is $81$

Thus, she obtained $81$ as an average of her scores.

Note: Mean is an essential concept in mathematics and statistics. The mean is the average or the most common value in a collection of numbers. In statistics, it is a measure of central tendency of a probability distribution along median and mode. It is also referred to as an expected value.
It is of three types.
Arithmetic Mean
Geometric Mean
Harmonic Mean
If we are said to find out the mean, it generally refers to the arithmetic mean.