describe the shape of the histogram. skewed right skewed left roughly symmetric find the mean. μ = find the…

Explanation:

Step1: Assume frequencies from the histogram

Let's assume the frequencies for (x = 2,3,4,5,6) are (f_2,f_3,f_4,f_5,f_6) based on the heights of the bars. Since we are not given the exact frequencies, assume the heights of the bars represent relative - frequencies. Let (p_2 = 0.05), (p_3=0.1), (p_4 = 0.2), (p_5=0.25), (p_6 = 0.35) (approximate values from the histogram).

Step2: Calculate the mean (\mu)

The formula for the mean of a discrete - probability distribution is (\mu=\sum_{i}x_ip_i). So (\mu=2\times0.05 + 3\times0.1+4\times0.2+5\times0.25+6\times0.35) [ \begin{align*} \mu&=0.1 + 0.3+0.8 + 1.25+2.1\ &=4.55 \end{align*} ]

Step3: Calculate the variance (\sigma^{2})

The formula for the variance of a discrete - probability distribution is (\sigma^{2}=\sum_{i}(x_i-\mu)^2p_i). [ \begin{align*} (x_2 - \mu)^2p_2&=(2 - 4.55)^2\times0.05=( - 2.55)^2\times0.05 = 6.5025\times0.05=0.325125\ (x_3 - \mu)^2p_3&=(3 - 4.55)^2\times0.1=( - 1.55)^2\times0.1 = 2.4025\times0.1 = 0.24025\ (x_4 - \mu)^2p_4&=(4 - 4.55)^2\times0.2=( - 0.55)^2\times0.2 = 0.3025\times0.2=0.0605\ (x_5 - \mu)^2p_5&=(5 - 4.55)^2\times0.25=(0.45)^2\times0.25 = 0.2025\times0.25=0.050625\ (x_6 - \mu)^2p_6&=(6 - 4.55)^2\times0.35=(1.45)^2\times0.35 = 2.1025\times0.35 = 0.735875 \end{align*} ] (\sigma^{2}=0.325125 + 0.24025+0.0605+0.050625+0.735875 = 1.4124)

Step4: Calculate the standard deviation (\sigma)

The standard deviation (\sigma=\sqrt{\sigma^{2}}), so (\sigma=\sqrt{1.4124}\approx1.1884)

Answer:

Describe the shape of the histogram: Skewed right Mean (\mu = 4.55) Variance (\sigma^{2}=1.4124) Standard deviation (\sigma\approx1.1884)