Question

i provided the formulas

1. Relevant formulas for this test are listed below. 1. Mean - (EX) N 2. Range - max-min 3. Variance = $$ (for a population) or (for a sample) 4. Standard deviation - Vo? (for a population) or 2 (for a sample) SS or DF SS N-1

Answer 1

Question 1

The required formula for finding the mean is:

Mean = (ΣX) / N

For the given data set:

• ΣX = 13 + 15 + 17 + 18 + 19 = 82
• N = 11

Hence, mean = 82 / 11 = 7.455 (approx.)

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Question 2

As N = 11 (odd) here, the middle / median value of the data set will be given by the X value corresponding to the 0.5 (N + 1)^th F value.

Here, 0.5 (N + 1)^th F value = 0.5 (11 + 1)^th = 6^th F value.

Now, the 6^th F value corresponds to X = 17 (because F represents frequency and the value of X from the 4^th to 7^th positions is X = 17).

Hence, the median of the given data set is 17.

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Question 3

The mode of a data set represents the most repeated X value in the data set, i.e. the X value having the highest frequency.

From the given data, it is evident that X = 17 has the highest frequency (F = 4) amongst all.

Hence, the mode of the given data set is 17.

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Question 4

For a population, the applicable formula for variance (σ²) is:

σ² = SS / N

For the given data set:

• SS = 44.54
• N = 11

Hence, σ² = 44.54 / 11 = 4.0491 (approx.)

Now, the standard deviation (σ) is simply the positive square root of the above variance.

Hence, standard deviation (σ) = (4.0491)^0.5 = 2.0122 (approx.)

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Question 5

For a sample, the applicable formula for variance (s²) is:

s² = SS / (N - 1)

For the given data set:

• SS = 44.54
• (N - 1) = (11 - 1) = 10

Hence, s² = 44.54 / 10 = 4.454

Now, the standard deviation (s) is simply the positive square root of the above variance.

Hence, standard deviation (s) = (4.454)^0.5 = 2.1105 (approx.)

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Hope this helps!