Respuesta :
In the given set of data, mean is 0.352, range is 0.86, median is 0.31, interquartile range is 0.28, mode is 0.12 and 0.24, and standard deviation is 0.81.
What is a data set?
A data set is a certain number of data given in any order.
Given, the measurements for 13 children are: 0.10, 0.25, 0.50, 0.4, 0.12, 0.12, 0.24, 0.24, 0.31, 0.36, 0.42, 0.55, 0.96.
By rearranging the data set in ascending order we get:
(0.10, 0.12, 0.12, 0.24, 0.24, 0.25, 0.31, 0.36, 0.4, 0.42, 0.50, 0.55, 0.96.)
1. Therefore, mean
= (0.10 + 0.25 + 0.50 + 0.4 + 0.12 + 0.12 + 0.24 + 0.24 + 0.31 + 0.36 + 0.42 + 0.55 + 0.96)/13
= 4.57/13
= 0.352
2. Therefore, range
= (0.96 - 0.10)
= 0.86
3. Therefore, median = 0.31
4. Here, median of the first half of the data set is
= Q₁
= (0.12 + 0.24)/2
= 0.18
Again, median of the second half of the data set is
= Q₃
= (0.42 + 0.50)/2
= 0.46
Therefore, the interquartile range
= (Q₃ - Q₁)
= (0.46 - 0.18)
= 0.28
5. Therefore, mode = 0.12, 0.24
6. Therefore, standard deviation is
= √[(x₁ - X)² + (x₂ - X)² + (x₃ - X)² + (x₄ - X)² + (x₅ - X)² + (x₆ - X)² + (x₇ - X)² + (x₈ - X)² + (x₉ - X)² + (x₁₀ - X)² + (x₁₁ - X)² + (x₁₂ - X)² + (x₁₃ - X)²]
Here, x₁, x₂,......, x₁₃ are given data set in ascending order.
X = mean of the given data set.
Therefore, standard deviation is
= √[(0.10 - 0.352)² + (0.12 - 0.352)² + (0.12 - 0.352)² + (0.24 - 0.352)² + (0.24 - 0.352)² + (0.25 - 0.352)² + (0.31 - 0.352)² + (0.36 - 0.352)² + (0.40 - 0.352)² + (0.42 - 0.352)² + (0.50 - 0.352)² + (0.55 - 0.352)² + (0.96 - 0.352)²]
= √[.064 + 0.054 + 0.054 + 0.013 + 0.013 + 0.01 + 0.0018 + 0.00006 + 0.0023 + 0.0046 + 0.023 + 0.039 + 0.37]
= √(.6488)
= 0.81
Learn more about data set here: https://brainly.com/question/15607085
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