Answer to Question #347795 in Statistics and Probability for Johny Blake

Question

Find (a) the mean, (b) the median, (c) the mode, and (d) the midrange.

Observers in the Frogwatch Program. The number of observers in the Frogwatch USA

program (a wildlife conservation program dedicated to helping conserve frogs and toads) for the

top 10 states with the most observers is 484, 483, 422, 396, 378, 352, 338, 331, 318, and 302. The

top 10 states with the most active watchers list these numbers of visits: 634, 464, 406, 267, 219,

194, 191, 150, 130, and 114. Compare the measures of central tendency for these two groups of

data

Answer 1

Sorted Data Set: 

$$302, 318, 331, 338, 352, 378, 396, 422, 483, 484$$

Sorted Data Set: 

$$114, 130, 150, 191, 194, 219, 267, 406, 464, 634$$

(a)

$$mean_1=\dfrac{1}{10}(302+318+331+338+352$$

$$+378+396+422+483+484)=380.4$$

$$mean_2=\dfrac{1}{10}(114+130+150+191+194$$

$$+219+ 267+406+464+634)=276.9$$

$$mean_1>mean_2$$

(b)

$$median_1=\dfrac{352+378}{2}=365$$

$$median_2=\dfrac{194+219}{2}=206.5$$

$$median_1>median_2$$

(c)

$$mode_1=undefined,$$

All values appeared just once.

$$mode_2=undefined,$$

All values appeared just once.

(d)

$$midrange_1=\dfrac{302+484}{2}=393$$

$$midrange_2=\dfrac{114+634}{2}=374$$

$$midrange_1>midrange_2$$