Question

for the given histograms, which of the following correctly orders the standard deviations of the distributions from least to greatest? a) a, b, c b) b, a, c c) a, c, b d) b, c, a e) c, a, b
data sets x and y are shown in the histograms. which of the following statements must be true? a) the ranges of data set x and data set y are equal. b) the medians of data set x and data set y are equal. c) the means of data set x and data set y are equal. d) the standard deviation of data set x is greater than the standard deviation of data set y. e) all of these must be true.

Explanation:

Step 1: Understand standard - deviation concept

Standard deviation measures the spread of data. Data more clustered has lower standard - deviation.

Step 2: Analyze Histogram A

Histogram A has data more spread out compared to B.

Step 3: Analyze Histogram B

Histogram B has data more clustered around the center, so it has the lowest standard - deviation among the three.

Step 4: Analyze Histogram C

Histogram C has data more spread out than B but less than A.

for second question:

Step 1: Analyze range

The range is the difference between the maximum and minimum values. Just from the histograms, we can't be sure the ranges are equal as we don't know exact max and min values precisely.

Step 2: Analyze median

The median is the middle - value. The shapes of the histograms don't guarantee equal medians.

Step 3: Analyze mean

The mean is the sum of all values divided by the number of values. The histograms don't provide enough information to say means are equal.

Step 4: Analyze standard deviation

Data set X has more extreme values (tails) compared to data set Y. Data set X is more spread out, so the standard deviation of data set X is greater than that of data set Y.

Answer:

B) B, A, C