Question

describe the shape of the histogram. skewed right skewed left roughly symmetric find the mean. μ = 4.55 find the variance. σ² = 1.4124 find the standard deviation. round to four decimal places, if necessary. σ = 1.1884

Explanation:

Step1: Observe histogram shape

The tail of the histogram extends to the right, so it is skewed right.

Step2: Calculate mean formula

Assume the mid - points of the intervals are $x_i$ and the frequencies are $f_i$. The mean $\mu=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}$. Without the actual frequency values, we can't calculate the exact mean. But if we had them, we'd multiply each mid - point by its frequency, sum those products, and divide by the total frequency.

Step3: Calculate variance formula

The variance $\sigma^{2}=\frac{\sum_{i = 1}^{n}f_i(x_i-\mu)^{2}}{\sum_{i = 1}^{n}f_i}$. After finding the mean, we'd subtract the mean from each mid - point, square the result, multiply by the frequency, sum those values, and divide by the total frequency.

Step4: Calculate standard deviation formula

The standard deviation $\sigma=\sqrt{\sigma^{2}}$, which is the square root of the variance.

Answer:

Describe the shape of the histogram: Skewed right
Find the mean: (Can't be calculated without frequency data)
Find the variance: (Can't be calculated without frequency data)
Find the standard deviation: (Can't be calculated without frequency data)