Answer to Question #286437 in Statistics and Probability for sarrah

Question

233.8 316.5 284.6247.3 317.6 280.3 231.9 255.3 258.4 276.9 278.9 269.3 263.9 289.3 280.6 277.8 268.8 306.3 308.3 292.8 232.4

302.5 293.4 237.2 299.2 290.2 234.5 260.9 240.7 249.1 240.5 232.8 254.3 264.2 298.7 274.1 247.2 287.0 318.9 312.2 252.5 304.3

274.1 252.2 266.2 296.6 251.3 274.8 290.9

270.3

 

1. Measures of central tendency
2. Measures of variation
3. Measure of position
4. Shape of data distribution

Answer 1

Solution:

Here we are given that,

X = {233.8 316.5 284.6247.3 317.6 280.3 231.9 255.3 258.4 276.9 278.9 269.3 263.9 289.3 280.6 277.8 268.8 306.3 308.3 292.8 232.4 302.5 293.4 237.2 299.2 290.2 234.5 260.9 240.7 249.1 240.5 232.8 254.3 264.2 298.7 274.1 247.2 287.0 318.9 312.2 252.5 304.3 274.1 252.2 266.2 296.6 251.3 274.8 290.9 270.3}

Variable N N* Mean SE StDev Variance CoefVar  

X 50 0 272.84 3.60 25.43 646. 9.32

Variable Sum of Squares Minimum Q1 Median Q3 Maximum Range

X 3753659.40 231.90 251.98 274.10 292.95 318.90 87.00

N for

Variable IQR Mode Mode Skewness Kurtosis

X 40.98 274.1 2 0.05 -1.02

A)Find measures of central tendency:-

Ans:-

There are three main measures of central tendency: the mode, the median and the mean. Each of these measures describes a different indication of the typical or central value in the distribution.

Mean=272.84

Mode=274.1

Median=274.1

B)Find Measure of variation:-

Ans:-

Variability is most commonly measured with the following descriptive statistics:

Range: the difference between the highest and lowest values.

Interquartile range: the range of the middle half of a distribution.

Standard deviation: average distance from the mean.

Variance: average of squared distances from the mean.

Minimum value=231.90

Maximum value=318.90

Range=Max-Min=318.90-231.90=87

Q1=1st Quartile=251.98

Q3=3rd Quartile=292.95

Therefore,

IQR=Interquartile range$=\dfrac{Q3-Q1}2=\dfrac{292.95-251.98}2=\dfrac{40.97}2=20.485$

Therefore,

IQR=20.485=20.49

Variance=646.64

Standard deviation=25.43

C)Find Measure of position:-

Measures of position give us a way to see where a certain data point or value falls in a sample or distribution. A measure can tell us whether a value is about the average, or whether it's unusually high or low. Measures of position are used for quantitative data that falls on some numerical scale.

The most common measures of position are percentiles, quartiles, and standard scores.

Q1=1st Quartile=251.98

Q2=2nd Quartile=Median=274.1

Q3=3rd Quartile=292.95

25 th Percentile=251.975

50 th Percentile=274.1

90 th Percentile=308.1

D)Shape of the Distribution:-

Box-Plot:-

Histogram:-

Therefore,

Shape of the distribution is symmetric.