The accompanying histogram shows the lengths of hospital stays (in days) for all female patients admitted to a certain hospital during one year with a primary diagnosis of acute myocardial infarction (heart attack). Complete parts (a) through (c) below. a) From the histogram, determine whether the mean or median is larger. Explain. A.Because the distribution isnearly symmetric,the mean is expected to belargerthan the median. B.Because the distribution isnearly symmetric,the mean is expected to be about the same as the median. C.Because the distribution isskewed to the high end,the mean is expected to belargerthan the median. D.Because the distribution isskewed to the high end,the mean is expected to besmallerthan the median. E.Because the distribution isskewed to the low end,the mean is expected to belargerthan the median. F.Because the distribution isskewed to the low end,the mean is expected to besmallerthan the median.b) Write a few sentences describing this distribution (shape, center, spread, unusual features). Is the histogram uniform, unimodal, bimodal, or multimodal? A.The histogram is multimodal. B.The histogram is uniform. C.The histogram is unimodal. D.The histogram is bimodal.What is the center of the histogram? A.The center of the histogram is day15. B.The center of the histogram is day8. C.The center of the histogram is day 1. D.The center of the histogram is day5.What is the spread of the distribution as defined by the range? The data range fromnothingtonothingdays.(Type whole numbers. Use ascending order.)Describe any unusual features. A.There are many outliers. B.Some of the data values are significantly different from the other data. C.There is a peak at day 1, which may represent patients who did not survive. D.There are no unusual features for this distribution.c) Which summary statistics should be chosen to summarize the center and spread in these data? Why? The▼ meanmedianand▼ standard deviationIQRshould be chosen because▼ the distribution is skewed.the distribution is nearly symmetric.the data are quantitative.the data are categorical. Lengths of Hospital Stays600-Q400-200-51015Stay (days)PrintDone# of Female Patients

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Description: The accompanying histogram shows the lengths of hospital stays (in days) for all female patients admitted to a certain hospital during one year with a primary diagnosis of acute myocardial infarction (heart attack). Complete parts (a) through (c)

Answered: Q 600- 400- 200- 10 15 Stay (days) # of…

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The accompanying histogram shows the lengths of hospital stays (in days) for all female patients admitted to a certain hospital during one year with a primary diagnosis of acute myocardial infarction (heart attack). Complete parts (a) through (c) below.

a) From the histogram, determine whether the mean or median is larger. Explain.

Because the distribution is

nearly symmetric,

the mean is expected to be

larger

than the median.

Because the distribution is

nearly symmetric,

the mean is expected to be about the same as the median.

Because the distribution is

skewed to the high end,

the mean is expected to be

larger

than the median.

Because the distribution is

skewed to the high end,

the mean is expected to be

smaller

than the median.

Because the distribution is

skewed to the low end,

the mean is expected to be

larger

than the median.

Because the distribution is

skewed to the low end,

the mean is expected to be

smaller

than the median.

b) Write a few sentences describing this distribution (shape, center, spread, unusual features).

Is the histogram uniform, unimodal, bimodal, or multimodal?

The histogram is multimodal.

The histogram is uniform.

The histogram is unimodal.

The histogram is bimodal.

What is the center of the histogram?

The center of the histogram is day

15.

The center of the histogram is day

The center of the histogram is day 1.

The center of the histogram is day

What is the spread of the distribution as defined by the range?

The data range from

nothing

days.

(Type whole numbers. Use ascending order.)

Describe any unusual features.

There are many outliers.

Some of the data values are significantly different from the other data.

There is a peak at day 1, which may represent patients who did not survive.

There are no unusual features for this distribution.

c) Which summary statistics should be chosen to summarize the center and spread in these data? Why?

The

▼

mean

median

and

▼

standard deviation

IQR

should be chosen because

▼

the distribution is skewed.

the distribution is nearly symmetric.

the data are quantitative.

the data are categorical.

Lengths of Hospital Stays
600-
Q
400-
200-
5
10
15
Stay (days)
Print
Done
# of Female Patients

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Q 600- 400- 200- 10 15 Stay (days) # of Female Patients