Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?
2 answers:
Answer:
Refer to the figure attached.
Detailed explanation:
Here are several pointers for relating the histogram to the mean and median.
1) In cases where the histogram shows a right skew, the mean exceeds the median.
2) When the histogram nearly resembles a symmetrical shape, the mean and median will be relatively similar.
3) In situations where the histogram is skewed to the left, the mean will fall below the median.
Thus, based on the provided data, the median is 29.5, and the mean approximates this value.
Consequently, it indicates that the histogram is nearly symmetric.
Therefore, the data set that probably has a mean closest to 29.5 is represented in the accompanying figure.
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Answer:
A) The estimated proportion of women whose platelet counts fall within 2 standard deviations of the mean, or between 118.5 and 377.3, is 95%.
B) The estimated percentage of women with platelet counts ranging from 53.8 to 442.0 is 99.7%.
Step-by-step explanation:
Provided data:
mean;μ = 247.9
standard deviation;σ = 64.7
A) We seek to find the estimated percentage of women with platelet counts within 2 standard deviations from the mean, which translates to values between 118.5 and 377.3.
Based on the attached image, the empirical curve indicates that the likelihood within 1 standard deviation of the mean is (34% + 34%) = 68%.
In contrast, the likelihood within 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%
Therefore, the estimated percentage of women having platelet counts within 2 standard deviations of the mean, or ranging from 118.5 to 377.3, equals 95%
B) Next, we want to determine the estimated percentage of women with platelet counts between 53.8 and 442.0.
The values of 53.8 and 442.0 correspond to 3 standard deviations from the mean.
Let’s verify that.
Since mean;μ = 247.9
standard deviation;σ = 64.7;
μ = 247.9
σ = 64.7
μ + 3σ = 247.9 + 3(64.7) = 442
Also;
μ - 3σ = 247.9 - 3(64.7) = 53.8
From the attached empirical curve, it can be seen that at 3 standard deviations from the mean, the probability percentage is;
(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%
