Page 128 - Data Science class 10
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Let us continue understanding the relationship between mean, median, and mode formula with the help of an
example.
Example 1.9: It is given that in a moderately skewed distribution, median = 10 and mean = 12. Using these values,
find the approximate value of mode.
Solution: Let us take mode to be ‘x’. We have been given that the median = 10 and mean = 12. Now, using the
relationship between mean mode and median we get, (Mean – Mode) = 3 (Mean – Median)
So, 12 – x = 3 (12 – 10)
12 – x = 3 × 2
12 – x = 6
–x = –6 or x = 6
So, Mode = 6
1.6. STANDARD DEVIATION
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard
deviation means that the data are grouped around the mean, whereas a high standard deviation means that the
data are more dispersed. While a high or low standard deviation indicates that data points are, respectively, above
or below the mean, one that is near zero suggests that data points are close to the mean.
1.6.1. Calculating the Standard Deviation
Standard deviation is calculated as follows:
• Find the mean by adding up all the data parts and dividing it by the number of parts of the data.
• Subtract mean from each value.
• Calculate the square of each of the differences.
• Find the average of squared numbers calculated in previous point to find the variance.
• Finally, find the square root of the variance. That is the standard deviation.
Example 1.10: Find the Standard Deviation where, we have the data points 5, 7, 3, and 7.
Step 1 Find the mean.
5 + 7 + 3 + 7
=
4
22
=
4
= 5.5
This leads to the following determinations: x ̄ = 5.5 and N = 4
Step 2 Subtract mean from each value.
We get:
5 – 5.5 = –0.5
7 – 5.5 = 1.5
3 – 5.5 = –2.5
7 – 5.5 = 1.5
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