Question

1)What are the strengths and limitations of the range?

2)Can the measures of central tendency and the measures of spread be used together to describe a set of scores? If so, how?

3) How are the standard deviation and the variance similar ? how are they different ?

Answer 1

1) Range:

In statistics, the range of a set of data is the difference between the largest and smallest values.^[1] Difference here is specific, the range of a set of data is the result of subtracting the smallest value from largest value.

Merits or strengths :

1. It is easiest to calculate and simplest to understand even for a beginner.

2. It is one of those measures which are rigidity defined.

3. It gives us the total picture of the problem even with a single glance.

4. It is used to check the quality of a product for quality control. Range plays an important role in preparing R- charts, thus quality is maintained.

5. The idea about the price of Gold and Shares is also made taking care of the range in which prices have moved for the past some periods.

6. Meteorological Dep’t. Also makes forecasts about the weather by keeping range of temp, in view.

B. Demerits or Limitations:

1. Range is not based on all the terms. Only extreme items reflect its size. Hence range cannot be completely representative of the data as all other middle values are ignored.

2. Due to above reason range is not a reliable measure of dispersion.

3. Range does not change even the least even if all other, in between, terms and variables are changed…

4. Range is too much affected by fluctuation of sampling. Range changes from sample to sample. As the size of sample increases range increases and vice versa.

5. It does not tell us anything about the variability of other data.

6. For open-end intervals, range is indeterminate because lower and upper limits of first and last interval are not given

2) Yes the  measures of central tendency and the measures of spread be used together because both are depend on the data or we can both are calculated on same data

where Measures of spread include the range, quartiles and the interquartile range, variance and standard deviation.

Dataset A	Dataset B
4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8	1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11

and

In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.

Mean

The mean is the arithmetic average, and it is probably the measure of central tendency that you are most familiar. Calculating the mean is very simple. You just add up all of the values and divide by the number of observations in your dataset.

Median

The median is the middle value. It is the value that splits the dataset in half. To find the median, order your data from smallest to largest, and then find the data point that has an equal amount of values above it and below it. The method for locating the median varies slightly depending on whether your dataset has an even or odd number of values.

Mode

The mode is the value that occurs the most frequently in your data set. On a bar chart, the mode is the highest bar. If the data have multiple values that are tied for occurring the most frequently, you have a multimodal distribution. If no value repeats, the data do not have a mode.

3)

standard deviation and the variance are not similler because standard  deviation is a square root of variance hence both are different and units are different

example height of students is in meter square if we take square root then it will be meter hence both are diffrent.

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