Interpreting Data and Making Predictions

Show your work for each problem.

1.
A store had 50 customers on Monday, 65 on Tuesday, and 80 on Wednesday. What type of trend does this show?
1. a)Decreasing trend
2. b)Increasing trend
3. c)No trend (constant)
4. d)Unpredictable pattern
Answer: Increasing trend
The numbers go from 50 to 65 to 80, which means they are increasing each day. This is an increasing (upward) trend.
2.
A plant's height was recorded each week: Week 1: 4 cm, Week 2: 7 cm, Week 3: 10 cm. By how many centimeters does the plant grow each week?
Answer: 3
From Week 1 to Week 2: $7 - 4 = 3$ cm. From Week 2 to Week 3: $10 - 7 = 3$ cm. The plant grows 3 cm each week.
3.
Ice cream sales and swimming pool attendance both increase during summer. This is an example of:
1. a)A decreasing trend
2. b)Correlation without causation
3. c)Swimming causing ice cream sales
4. d)Ice cream causing swimming
Answer: Correlation without causation
This is correlation without causation. Ice cream doesn't make people swim, and swimming doesn't make people buy ice cream. Hot summer weather causes both to increase independently.
4.
A baker sold 20 loaves on Monday, 25 on Tuesday, and 30 on Wednesday. How many loaves should they predict for Thursday if the pattern continues?
Answer: 35
1. What is the increase from Monday to Tuesday? 5
2. What is the increase from Tuesday to Wednesday? 5
3. Is there a consistent pattern? yes
4. Using the pattern, predict Thursday's sales 35
5.
A student's test scores are: 82, 85, 45, 88, 91, 86, 84, 89. The score of 45 is much lower than the others. What should we call this score?
1. a)A trend
2. b)A correlation
3. c)An outlier
4. d)A prediction
Answer: An outlier
An outlier is a data point that is significantly different from other values. The score of 45 is noticeably lower than the other scores (82, 84, 85, 86, 88, 89, 91), making it an outlier.
6.
A company's monthly profits were: January 12000, February 15000, March 18000, April 21000. What would you predict for May if the pattern continues? Enter only the number.
Answer: 24000
The pattern shows profits increasing by 3000 each month: $12000 \to 15000 \to 18000 \to 21000$ . Adding 3000 to April: $21000 + 3000 = 24000$ .
7.
Calculate the average (mean) of these daily temperatures: 18, 22, 20, 24, 16 degrees Celsius.
Answer: 20
1. Add all the temperatures together 100
2. How many data values are there? 5
3. Divide the sum by the count to find the average 20
8.
A scientist has only 2 data points and wants to make a prediction. Why might this be unreliable?
1. a)Predictions don't need patterns
2. b)Two points always give perfect predictions
3. c)The sample size is too small to establish a reliable pattern
4. d)More data would make it less accurate
Answer: The sample size is too small to establish a reliable pattern
With only 2 data points, you cannot determine if you're seeing a real pattern or random variation. More data points are needed to establish a reliable pattern for making predictions.
9.
A café tracked coffee sales: Mon 80, Tue 95, Wed 110, Thu 125. What is the range of these sales, and what do you predict for Friday?
Answer: 140
1. What is the highest value? 125
2. What is the lowest value? 80
3. What is the range (highest minus lowest)? 45
4. What is the daily increase? 15
5. Predict Friday's sales 140
10.
Alex's grades: 70, 75, 80, 85. Jordan's grades: 90, 88, 86, 84. If these trends continue for two more tests, who will have the higher score on Test 6?
1. a)Alex (95) vs Jordan (80)
2. b)They will tie at 85
3. c)Alex (90) vs Jordan (82)
4. d)Jordan will still be higher
Answer: Alex (95) vs Jordan (80)
Alex: +5 per test → Test 5: 90, Test 6: 95. Jordan: -2 per test → Test 5: 82, Test 6: 80. Alex overtakes Jordan and scores 95 vs 80 on Test 6.
11.
A runner's lap times (in seconds) were: 65, 62, 59, 56. What would be the predicted time for the 6th lap if the pattern continues?
Answer: 50
Each lap is 3 seconds faster: 65 → 62 → 59 → 56. Lap 5: $56 - 3 = 53$ seconds. Lap 6: $53 - 3 = 50$ seconds.
12.
A store's weekly sales were: Week 1: 200, Week 2: 240, Week 3: 280, Week 4: 320. Calculate the average weekly sales and predict Week 6 sales.
Answer: 400
1. What is the sum of all four weeks? 1040
2. What is the average weekly sales? 260
3. What is the weekly increase in sales? 40
4. Predict Week 5 sales 360
5. Predict Week 6 sales 400
13.
A weather app predicts it will be 25 degrees Celsius tomorrow based on a pattern. The actual temperature could be different because:
1. a)Patterns always give exact predictions
2. b)Weather conditions can change unexpectedly
3. c)Apps always predict incorrectly
4. d)Temperature never changes
Answer: Weather conditions can change unexpectedly
Predictions are based on patterns, but real-world conditions can change unexpectedly. A storm, cold front, or other weather event could make the actual temperature different from the prediction. This is why predictions become less reliable further into the future.
14.
Two teams tracked their points over 4 games. Team A: 45, 50, 55, 60. Team B: 70, 65, 60, 55. After which game does Team A first lead Team B?
Answer: 4
1. What is Team A's pattern per game? +5
2. What is Team B's pattern per game? -5
3. In Game 3, what are the scores? (A, B) 55, 60
4. In Game 4, what are the scores? (A, B) 60, 55
5. After which game does A first lead? 4
15.
A data set has values: 8, 12, 15, 21, 4. What is the range of this data? (Highest minus lowest)
Answer: 17
Highest value: 21. Lowest value: 4. Range: $21 - 4 = 17$ .
16.
A farmer counts eggs each day: Mon 12, Tue 15, Wed 18, Thu 21. If the pattern continues, how many total eggs will there be from Monday through Friday?
Answer: 90
1. What is the daily increase in eggs? 3
2. Predict Friday's egg count 24
3. Add all five days together 90