Question

mean: 459
median: 468

number of likes
however, in the last week, the analysis showed a big dropoff in views, with only 12 likes.

number of likes
question 1: which of the lines (a, b, c, or d) shown above is most likely to be the mean after including the dropoff in views?
a
b
c
d
question 2: which of the lines (a, b, c, or d) is most likely to be the median after including the dropoff in views?
a
b
c
d
question 3: which of the following descriptive statistics are strongly affected by outliers? choose all that apply.
mode
average
median
range
question 4: in which of the cases should paloma throw out or change the outlier? choose all that apply.
the cause was that paloma got the flu and made almost no posts
the social media company issued a correction on the number of likes for the week
by mistake, when entering the number of likes, paloma failed to input the last digit
for the next post, of a squirrel eating a cupcake, the number of likes shot up even higher than they were before

Explanation:

Step1: Count original data points

From the top plot, there are 6 data points (the blue dots: 2 at ~400, 4 at ~480).

Step2: Calculate original total likes

Original mean = 459, so total = $459 \times 6 = 2754$.

Step3: Calculate new mean with outlier

Add the 12 likes: new total = $2754 + 12 = 2766$, new count = 7.
New mean: $\frac{2766}{7} \approx 395.14$, which is closest to line C.

Step4: Find new median

Original 6 data points sorted: $x_1, x_2, x_3, x_4, x_5, x_6$ (median is $\frac{x_3+x_4}{2}=468$). Add 12, sorted data: $12, x_1, x_2, x_3, x_4, x_5, x_6$. The 4th value ($x_3$) is the median, close to original median (line D).

Step5: Identify outlier-sensitive stats

Mean (average) uses all values, range depends on min/max; median/mode are robust.

Step6: Determine valid outlier exclusion

Outliers are removed only if they are errors or non-representative of the dataset's purpose.

Answer:

1. C
2. D
3. Average, Range
4. The social media company issued a correction on the number of likes for the week; By mistake, when entering the number of likes, Paloma failed to input the last digit