Question

1) [5] Find the mean, median, variance, and standard deviation of the number of texts everyone in a family of six sent in a month. Show all work including a table like we created in class. Find answers to one decimal place. Be sure to use the appropriate symbols. Data: 162 40 129 61 68 107

Answer 1

	Number of texts	deviation	(deviation)^2
	162	67.5	4556.25
	40	-54.5	2970.25
	129	34.5	1190.25
	61	-33.5	1122.25
	68	-26.5	702.25
	107	12.5	156.25
Total	567		10697.5
Mean	94.5		2139.5	Variance
			46.3	Std Dev

Here deviation = Xi-H, where u is the mean.

Formula for mean n

Formula for median : If the number of observations is even then the median is average of the two middle observations. Here, n= 6 (even), so, the median will be average of the two middle observations. For this, we first write the observations in ascending order and then take the average of the two middle observations. 40, 61, 68, 107, 129, 162 Hence, the median is average of 68 and 107, which is, 68 + 107 o -= 87.5

Here the variance is calculated using the formula 2-1 (I; - u) n-1 Some books use the formula 2-1(1; – u)2 m i lf the 2nd formula is used then 10697.5 variance = 6 = Standard deviation = V variance = V1782.9 = 42.2