Measures of central tendency/ measures of central location/ summary statistics seek to describe the presented data by identifying the central position within the given data set. The measures include the mean, median and mode. Variance and standard deviation represent the level of dispersion among the data given. The mean of the sample is given as follows

Where ∑x is the sum of the values given in the data set ,µ is the sample mean and n is the total number of values given

The following is the sum of the data given (∑x)

14.5+ 14.6+ 14.7+14.8+ 14.9+15.3+14.9+15.5+14.8+15.2+ 15+15.1+15+14.4+15.8+14+16+16.1+15.8+14.5+14.6+14.8+14.8+14.6+14.5+14.7+14.9+14+14.2+14.1=4

∑x =446.1

N=30

Mean =446.1/30=14.87

The median is calculated by finding the central value after arranging the values from the smallest to the largest

14, 14, 14.1, 14.2,14.4, 14.5,14.5,14.5, 14.6, 14.6, 14.6 14.7,14.7, 14.8, 14.8,14.8,14.8, 14.9, 14.9,14.9,15,15, 15.1, 15.2, 15.3, 15.5,15.8,15.8, 16, 16.1

Median==14.8

The mode is the value that appears the most number of times in the data set and the value is 14.8. The Value appears four times.

x f (x-mean) f(x-mean)2

14 2 -0.87 1.5138

14.1 1 -0.77 0.5929

14.2 1 -0.67 0.4489

14.4 1 -0.47 0.2209

14.5 3 -0.37 0.1369

14.6 3 -0.27 0.0729

14.7 2 -0.17 0.0578

14.8 4 -0.07 0.0196

14.9 3 0.03 0.027

15 2 0.13 0.0338

15.1 1 0.23 0.0529

15.2 1 0.33 0.1089

15.3 1 0.43 0.1849

15.5 1 0.63 0.3969

15.8 2 0.93 1.7298

16 1 1.13 1.2769

16.1 1 1.23 1.5129

Total= 30 9.0109

The data is from the sample hence the variance is given by the following formula

=9.0109/29=0.3107

Standard deviation is the square root of the variance

The standard deviation of the sample given is 0.5574

The upper and lower limit expresses the highest and lowest value of the mean at a particular confidence interval. It is the range within which the mean can exist at a given level of confidence. The 95 percent confidence interval for the data from the sample is calculated as follows:

Mean=14.87

Se=0.55574

The value of t-critical at 95% significance level = t (29, 0.05) = 0.2052

The Upper limit=Sample Mean plus se. (t-critical)

=14.87+0.5574(0.2052) = 14.9844

The lower limit is sample mean minus the se.(t-critical)

=14.87-0.5574(0.2052) = 14.7556

The 95% confidence interval can be given as:

P [14.76

Asked in Standards & Testing - 561 days ago

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Measures of Central Tendency

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