Respuesta :
Answer:
First quartile = 69
Variance = 107.46
Step-by-step explanation:
We are given the following data-set in the question:
71, 76, 69, 79, 89, 77, 64, 92, 68, 93, 72, 95, 79, 65, 84
- The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers.
- The first quartile, or 25th percentile is the number for which 25% of values in the data set are smaller it.
The sorted data is:
64, 65, 68, 69, 71, 72, 76, 77, 79, 79, 84, 89, 92,93, 95
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
Median or second quartile =
[tex]\displaystyle\frac{15+1}{2} = 8^{th}\text{ term} = 77[/tex]
Bottom half:
64, 65, 68, 69, 71, 72, 76
First quartile is the mid value of these number.
First quartile = 69
Formula:
[tex]\text{Variation} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
Sum of squares of differences = 1504.4
[tex]\text{Variance} = \frac{1504.4}{14} = 107.46[/tex]
