Question

maria ran an experiment to determine the optimal conditions for growing artichokes. the data below displays the weights of the artichokes she grew (measured in grams).
45.8 74.1 55.4 62.2 53.4 74.1 49 59 74.1 36.6

what is the mean weight of the artichokes?
mean = \boxed{} grams (round to two decimal places)

what is the median weight of the artichokes?
median = \boxed{} grams

what is the mode weight of the artichokes?
mode = \boxed{} grams

Explanation:

Mean Calculation

Step1: Sum all the weights

The weights are 45.8, 74.1, 55.4, 62.2, 53.4, 74.1, 49, 59, 74.1, 36.6. Let's sum them:
\( 45.8 + 74.1 + 55.4 + 62.2 + 53.4 + 74.1 + 49 + 59 + 74.1 + 36.6 \)
First, group like terms:
\( (45.8 + 36.6) + (74.1 + 74.1 + 74.1) + (55.4 + 53.4) + (62.2 + 49 + 59) \)
\( = 82.4 + 222.3 + 108.8 + 170.2 \)
\( = 82.4 + 222.3 = 304.7 \); \( 304.7 + 108.8 = 413.5 \); \( 413.5 + 170.2 = 583.7 \)

Step2: Divide by the number of data points

There are 10 data points. So mean \( = \frac{583.7}{10} = 58.37 \) (already rounded to two decimals? Wait, wait, wait—wait, let's recalculate the sum correctly. Maybe I made a mistake. Let's add each number:

45.8 + 74.1 = 119.9
119.9 + 55.4 = 175.3
175.3 + 62.2 = 237.5
237.5 + 53.4 = 290.9
290.9 + 74.1 = 365
365 + 49 = 414
414 + 59 = 473
473 + 74.1 = 547.1
547.1 + 36.6 = 583.7. Yes, sum is 583.7. Number of data points: 10. So mean \( = \frac{583.7}{10} = 58.37 \) grams.

Median Calculation

Step1: Order the data

First, sort the weights in ascending order:
36.6, 45.8, 49, 53.4, 55.4, 59, 62.2, 74.1, 74.1, 74.1

Step2: Find the middle value(s)

Since there are 10 data points (even number), the median is the average of the 5th and 6th values.
5th value: 55.4; 6th value: 59.
Median \( = \frac{55.4 + 59}{2} = \frac{114.4}{2} = 57.2 \) grams.

Mode Calculation

Step1: Identify the most frequent value

Looking at the sorted data: 36.6, 45.8, 49, 53.4, 55.4, 59, 62.2, 74.1, 74.1, 74.1.
74.1 appears 3 times, which is more than any other value.

Answer:

s:
Mean: \( \boldsymbol{58.37} \) grams
Median: \( \boldsymbol{57.2} \) grams
Mode: \( \boldsymbol{74.1} \) grams