Page 184 - Data Science class 10
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Standard deviation, σ = 10
Mean marks, μ = 50
Using z score formula,
z score for secured marks = z = 80 – 50
10
= 30
10
= 3
z score for Rohan`s marks = 3
Activity 1
Find the value represented by a z-score of 3.403, given µ = 62 and σ = 4.20.
4.3.2. How do You Interpret a Z-Score?
The value of the z-score states you how many standard deviations you are away from the mean.
• If a z-score is equivalent to 0, it is on the mean.
• A positive z-score specifies that the raw score is higher than the mean average. For example, if a z-score is equal
to +3, it is 3 standard deviations above the mean.
• A negative z-score tells that the raw score is below the mean average. For example, if a z-score is equal to –5, it
is 5 standard deviations below the mean.
4.3.3. Why Is a Z-Score So Important?
The z-score is important because it tells you not only about the value but also where it falls in the distribution.
It is very useful to standardise the values of a normal distribution by changing them into a z-score because:
• It gives us a chance to calculate the probability of a value occurring within a normal distribution.
• Z-score permits us to compare two values that are from different samples.
4.4. CONCEPT OF PERCENTILE
Percentile is a number that represents the percentage of scores that fall at or below that number. You might know
that you scored 68 out of 80 in a test. But that number has no real meaning unless you know what percentile you
fall into. If you know that your score is in the 90th percentile, that means you scored better than 90% of people
who took the test.
A percentile can be defined as the percentage of the total ordered observations at or below it. As a result, the pth
percentile of a distribution is the value at or below which p percent of the ordered observations fall.
Consider the following dataset: [9, 10, 14, 18, 12, 24, 17, 22, 21, 26]
Here, if we want to find the percentile for element 24, we follow the steps given below:
• First of all, arrange the dataset in ascending order. Once sorted, the dataset will look like [9, 10, 12, 14, 17, 18,
21, 22, 24, 26].
• The number of values at or below the element 24 is 9. The total number of elements in the dataset is 10.
• Thus, according to the definition, 90 percent of the values are at or below the element 24. Thus, percentile for
the element 24 is 90 percentiles.
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